# maximum lateral area

## Cylinder of maximum volume and maximum lateral area inscribed in a cone

**Situation**

A right circular cylinder of radius r and height h is inscribed in a right circular cone of radius 6 m and height 12 m.

Part 1: Determine the radius of the cylinder such that its volume is a maximum.

A. 2 m

B. 4 m

C. 3 m

D. 5 m

Part 2: Determine the maximum volume of the cylinder.

A. 145.72 m^{3}

B. 321.12 m^{3}

C. 225.31 m^{3}

D. 201.06 m^{3}

Part 3: Determine the height of the cylinder such that its lateral area is a maximum.

A. 10 m

B. 8 m

C. 6 m

D. 4 m